That's a lot of different categories.

I like naval warfare games, but I tend towards the sim side, not the "experience being someone there" sort.

The naval warfare game that I have played the most of recently is Rule the Waves 3. That's definitely not an eye candy game, but it models the design and development of warships from 1880 into the Cold War, the construction of fleets, and the tactics when they meet, has a lot of flexibility to simulate different stuff.

The game that I'm most looking forward to being completed is Sea Power: Naval Combat in the Missile Age, which is presently still in Early Access and last time I played it still had a lot of unfinished work. Sort of a spiritual successor to Fleet Command/Jane's Fleet Command. Modern air and naval warfare.

It doesn't work on Linux, so I can't play it, but Command: Modern Operations is probably the most sim-oriented contemporary air/naval warfare program you can get.

Two other naval warfare games that I enjoy playing:

Cold Waters, which is a Cold War sub warfare game. It abstracts out a lot of the manual stuff that some other sub sims do. Covers the "hide, gather data, strike" bit.

Carrier Command 2. This is not a real-world oriented sim. You command an amphibious assault ship which can capture islands to gain resources, capture technology, and buy munitions, air and amphibious vehicles, and fight against another similar amphibious assault ship approaching you. I really like the untextured polygon aesthetic -- they make stuff look pretty even with just that. Need to manage a ton of vehicles and aircraft and production and logistics vessels and support craft concurrently; as the game continues on, the load increases. If you've played Hostile Waters: Antaeus Rising, sort of similar idea

both are based on Carrier Command. Not mission-oriented the way Hostile Waters is. It's really intended to be played multiplayer, which I've no interest in, but you can play single-player if you can handle the load of doing all the tasks. I had a surprising amount of fun banging away with this one. I really think that this game would have benefited from some rebalancing and further development

some gear just isn't all that useful, and I think that the game would make a magnificent base for a more-sophisticated-dynamic-campaign single-player-oriented game.

You mention Subnautica. I enjoyed that, though unlike the other games here, that's not really a naval warfare game, but it's certainly got a sea theme. I think I own the sequel, Subnautica: Below Zero, but haven't played it, but given that you don't mention it, I thought I would, as I'd assume that if you like the first game, you'd also enjoy the second.

Sunless Sea and its sequel Sunless Sea: Zubmariner is...hard to describe, more about providing a dark British Empire fantasy naval-themed game. Not naval warfare, but exploring a subterranean world...but it's got sea theming. Not much like everything else on here. Mostly about creating a mood

the gameplay isn't terribly deep.

It's not, strictly-speaking, a sea-based game, but Nebulous: Fleet Command is a sci-fi space-based fleet warfare game. A lot of the elements that you might want in a sea-based fleet naval warfare game are there, sensors, electronic warfare, weapons and countermeasures and such.

I think that those are the sea- or sea-associated games that I'd probably most recommend, myself.

EDIT: I have not yet gotten around to playing Dredge, but I've read enough positive comments on it that I'd suggest at least looking at it.